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FIITJEE L t d . , F I I T JEE Hou se, 2 9 -A , Ka l u Sa r a i , Sa r va p r i y a V i h a r , New De l h i -1 1 00 16 , Ph 461 06000 , 2 65694 93 , Fa x 265139 42 websi t e : w ww . f i i t j e e .c om

FULL TEST – II

Paper 2

Time Allotted: 3 Hours Maximum Marks: 243

Please read the instruct ions carefu l ly . You are a l lot ted 5 minutesspecif ical ly for th is purpose.

You are not a l lowed to leave the Examinat ion Hall before the end ofthe test.

INSTRUCTIONS

A. General Inst ruct ions

1. Attempt ALL the questions. Answers have to be marked on the OMR sheets.2. This question paper contains Three Parts.3. Part-I is Physics, Part-II is Chemistry and Part-III is Mathematics.4. Each part is further divided into two sections: Section-A & Section-B5. Rough spaces are provided for rough work inside the question paper. No additional sheets will be

provided for rough work.6. Blank Papers, clip boards, log tables, slide rule, calculator, cellular phones, pagers and electronic

devices, in any form, are not allowed.

B. Filling of OMR Sheet1. Ensure matching of OMR sheet with the Question paper before you start marking your answers

on OMR sheet.2. On the OMR sheet, darken the appropriate bubble with black pen for each character of your

Enrolment No. and write your Name, Test Centre and other details at the designated places.3. OMR sheet contains alphabets, numerals & special characters for marking answers.

C. Marking Scheme For All Three Parts.(i) Section-A (01 to 09) contains 09 multiple choice questions which have only one correct answer.

Each question carries +3 marks for correct answer and – 1 mar k for wrong answer.

Section-A (10 – 13) contains 4 Assertion-Reasoning (multiple choice questions) which haveonly one correct answer. Each question carries +3 marks for correct answer and

– 1 mar k for wrong answer.

Section-A (14 – 19) contains 2 paragraphs. Based upon paragraph, 3 multiple choice questionshave to be answered. Each question has only one correct answer and carries +4 marks forcorrect answer and – 1 mar k for wrong answer.

(ii) Section -B (1 – 03) contains 3 Matrix Match Type (4 × 4 Matrix) questions containing statementsgiven in 2 columns. Statements in the first column have to be matched with statements in thesecond column. Each question carries +6 marks for all correct answer. There is no negativemarking.

Name of the Candidate

Enrolment No.

A L L

I N D I A

T E S T

S E

R I E S

FIITJEE JEE (Advanced), 2014

F r o m C

l a s s r o o m / I n t e g r a t e d S c

h o o l P r o g r a m s 7 i n T o p 2 0 , 2 3 i n

T o p 1 0 0 , 5 4 i n T o p 3 0 0 , 1 0 6 i n T o

p 5 0 0 A l l I n d i a R a n k s &

2 3 1 4 S t u d e n t s f r o m C

l a s s r o o m

/ I n t e g r a t e d S c

h o o l P r o g r a m s &

3 7 2 3 S t u d e n t s f r o m A

l l P r o g r a m s h a v e b e e n A w

a r d e d a R a n k i n J E E ( A d v a n c e d ) ,

2 0 1 3

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AITS-FT-II-(Paper-2)-PCM-JEE(Advanced)/14


2

Useful Data

PHYSICS

Acceleration due to gravity g = 10 m/s2

Planck constant h = 6.6 1034 J-s

Charge of electron e = 1.6 1019 C

Mass of electron me = 9.1 1031 kg

Permittivity of free space 0 = 8.85 1012 C

2/N-m

2

Density of water water = 103 kg/m

3

Atmospheric pressure Pa = 105 N/m2

Gas constant R = 8.314 J K1 mol

1

CHEMISTRY

Gas Constant R = 8.314 J K1 mol1 = 0.0821 Lit atm K

1mol

1

= 1.987 2 Cal K1 mol1 Avogadro's Number Na = 6.023 10

23

Planck’s constant h = 6.625 1034 Js

= 6.625 10 –27

ergs1 Faraday = 96500 coulomb1 calorie = 4.2 joule1 amu = 1.66 10 –27 kg1 eV = 1.6 10 –19 J

Atomic No: H=1, He = 2, Li=3, Be=4, B=5, C=6, N=7, O=8,N=9, Na=11, Mg=12, Si=14, Al=13, P=15, S=16,Cl=17, Ar=18, K =19, Ca=20, Cr=24, Mn=25,Fe=26, Co=27, Ni=28, Cu = 29, Zn=30, As=33,Br=35, Ag=47, Sn=50, I=53, Xe=54, Ba=56,Pb=82, U=92.

Atomic masses: H=1, He=4, Li=7, Be=9, B=11, C=12, N=14, O=16,

F=19, Na=23, Mg=24, Al = 27, Si=28, P=31, S=32,Cl=35.5, K=39, Ca=40, Cr=52, Mn=55, Fe=56, Co=59,Ni=58.7, Cu=63.5, Zn=65.4, As=75, Br=80, Ag=108,Sn=118.7, I=127, Xe=131, Ba=137, Pb=207, U=238.

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FIITJEE L t d . , F I I T JEE Hou se, 2 9 -A , Ka l u Sa r a i , Sa r va p r i y a V i h a r , New De l h i -1 1 00 16 , Ph 461 06000 , 2 65 694 93 , Fa x 265139 42 websi t e : w ww . f i i t j e e .c om

3

P P h h y y s s i i c c s s PART – I

SECTION – A

Straight Objective Type

This section contains 9 multiple choice questions numbered 1 to 9. Each question has 4 choices (A),(B), (C) and (D), out of which ONLY ONE is correct.

1. Two identical cylindrical vessels with their bases at the same level each contains a liquid ofdensity . The height of the liquid in one vessel is h1 and that in other is h2. The area of eitherbase is A. Then the work done by gravity in equalizing the levels when the vessels are connected

(A) 2

1 2

1gA h h

4 (B) 2 21 2

1gA h h

4

(C) 2

1 2

1gA h h

2 (D) 2 21 2

1gA h h

2

2. An empty plastic box of mass m is found to accelerate up at a rate of g/6 when placed deepinside water. Then the mass of sand be filled in it so that it may accelerate down at a rate of g/6

(A)5

m2

(B)2

m5

(C)2

m3

(D)3

m2

3. The distance from the surface of the earth at which the acceleration due to gravity is the samebelow and above the surface of the earth

(A) e5 1 R (B) e5 1

R2

(C) e5 1 R

2

(D) e5 1 R

4. A ray is incident on a spherical body ( = 3) making an angle 60 with the normal drawn at thepoint of incidence. The ray after passing through sphere gets incident on the further surface ofsphere and get reflected and refracted. Then the angle between the reflected and refracted raysat this surface is(A) 45 (B) 90 (C) 120 (D) 150

Space for rough work

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5. A square loop of side a is projected at t = 0, with speed v0 into a regionhaving uniform magnetic field B, with velocity perpendicular to themagnetic field. Which of the following plots correctly represents thevariation of induced emf of loop with time

a

v0

4a

B

(A)

t

(B)

t

(C)

t

(D)

t

6. A block A of mass M = 2kg is connected to another block B of mass

1kg with a string and a spring of force constant k = 600 N/m asshown in the figure. Initially spring is compressed to 10 cm andwhole system is moving on a smooth surface with a velocity v = 1m/s. At any time thread is burnt, the velocity of block A, when B ishaving maximum velocity w.r.t. ground, is:(A) 0 (B) 1 m/s(C) 3 m/s (D) none of these

A mM B

1 m/s

7. A metallic chain with a length and whose ends are joined together is fitted onto a

wooden disc as shown in the figure. The disc rotates with a speed of n revolutionsper second. Then the tension of the chain T if its mass is m

(A) mn (B) 2mn

(C) 2mn2 (D) mn

2


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8. An object of mass m is projected with momentum P at such an angle that its maximum height (H)is 1/4th of its horizontal range (R). Its minimum kinetic energy in its path will be

(A)2p

8m (B)

2p

4m

(C)23p

4m

(D)2p

m

9. The distance of centre of mass from O of a uniform plate having quartercircular inner and outer boundaries of radii a and b from centre O.

(A)3 3

2 2

4 b a

3 b a

(B)3 3

2 2

4 2 b a

3 b a

(C)3 3

2 2

4 b a

b a

(D)3 3

2 2

4 2 b a

3 b a

a

b

O

Reasoning Type

This section contains4 questions

numbered 10 to 13. Each question contains STATEMENT-1(Assertion) and STATEMENT-2 (Reason). Each question has 4 choices (A), (B), (C) and (D) out of whichONLY ONE is correct.

10. STATEMENT-1: In isothermal quasi-static process, heat is absorbed or given out by the systemeven though at every state the gas is at the same temperature as that of the surroundingreservoir.and

STATEMENT-2: This is possible because of the infinitesimal difference in temperature betweenthe system and surrounding.(A) Statement-1 is True, Statement-2 is True; Statement -2 is a correct explanation for Statement-1.(B) Statement-1 is True, Statement-2 is True; Statement -2 is NOT a correct explanation for

Statement-1.

(C) Statement -1 is True, Statement-2 is False.(D) Statement -1 is False, Statement-2 is True.


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11. STATEMENT-1: Only longitudinal waves can propagate in gases.and

STATEMENT-2: The modulus of rigidity of gases is zero.(A) Statement-1 is True, Statement-2 is True; Statement -2 is a correct explanation for Statement-1.(B) Statement-1 is True, Statement-2 is True; Statement -2 is NOT a correct explanation for

Statement-1.

(C) Statement -1 is True, Statement-2 is False.(D) Statement -1 is False, Statement-2 is True.

12. STATEMENT-1: If the net external force on a system is zero, the net torque on the system isindependent of origin.and

STATEMENT-2: When the net force on a system is zero, net torque may or may not be zero.(A) Statement-1 is True, Statement-2 is True; Statement -2 is a correct explanation for Statement-1.(B) Statement-1 is True, Statement-2 is True; Statement -2 is NOT a correct explanation for

Statement-1.(C) Statement -1 is True, Statement-2 is False.(D) Statement -1 is False, Statement-2 is True.

13. STATEMENT-1: In a photocell experiment, the stopping potential increases when the cathode ischanged from cesium (Cs) metal to aluminium (A).

and STATEMENT-2: Stopping potential does not depend on the threshold wavelength.(A) Statement-1 is True, Statement-2 is True; Statement -2 is a correct explanation for Statement-1.(B) Statement-1 is True, Statement-2 is True; Statement -2 is NOT a correct explanation for

Statement-1.(C) Statement -1 is True, Statement-2 is False.(D) Statement -1 is False, Statement-2 is True.


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7

Comprehension Type

This section contains 2 groups of questions. Each group has 3 multiple choice question based on aparagraph. Each question has 4 choices (A), (B), (C) and (D) for its answer, out of which ONLY ONE iscorrect.

Paragraph for Question Nos. 14 to 16

Two long parallel wires carrying currents 2.5 amp and I amp in the same direction as shown in figure. Anelectron moving with a velocity 4 105 m/sec. as shown in figure and experiences a force of magnitude3.2 10-20 N at the point R. Then

14. The value of current I is(A) 2 amp.(B) 8 amp.(C) 4 amp.(D) 1 amp.

ev

RQP

3m 2m

2.5 A I A

15. The position between PR at which a third long parallel wire carrying current 2.5 amp may be

placed such that magnetic induction at R is zero.(A) at 1 m from R and the direction of current is inward.(B) at 1 m from R and the direction of current is outward(C) at 1 m from P and the direction of current is inward.(D) at 1 m from P and the direction of current is outward

16. The position not between PR but on the line joining PR at which a third long parallel wire carryingcurrent 2.5 amp may be placed such that magnetic induction at R is zero.(A) at a distance of 1m from R and the direction of current is outward.(B) at a distance of 1 m from R and the direction of current is inward(C) at a distance of 1 m from P and the direction of current is outward(D) at a distance of 1 m from P and the direction of current is inward


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A tube of length and radius R carries a steady flow of a fluid whose density is and viscosity . Thevelocity v of flow is given by v = v0[1 (r

2/R

2)], where r is the distance of flowing fluid from the axis. Then

17. Volume of fluid flowing across the section of tube in unit time is

(A) 201 v R4

(B) 201 v R2

(C) v0R2 (D) 20

1v R

8

18. Kinetic energy of the fluid within the volume of the tube is

(A) 2 201

R v6

(B) 2 201

R v8

(C) 2 201

R v4

(D) 2 201

R v3

19. The difference of pressure at the end of the tube is(A) 0

2

4 v

R

(B) 0

2

8 v

R

(C) 02

2 v

R

(D) 0

2

v

R


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9

SECTION – B

(Matching List Type)

This section contains 3 multiple choice questions. Each question has matching Column(s). The codesfor the Column(s) have choices (A), (B), (C) and (D) out of which ONLY ONE or MORE is/are co rrect .

1. Match the following:Column – I Column – II

(A) Linear combination of two SHM’s(p) T = 2

R

g and not T =

(B) y = A sin 1t + A sin (2t + ) (q) SHM for equal frequencies and amplitude(C) Time period of a pendulum of infinite length. (r) Superposition may not be a SHM always.(D) Maximum value of time period of an

oscillating pendulum.(s) amplitude will be 2 A for 1 = 2 and

phase difference of /2.

2. Match the following:

Column – I Column – II (A) Characteristic X-ray (p) Inverse photoelectric effect.(B) X-ray production (q) high potential difference(C) Cut-off wavelength (r) Moseley’s law(D) Continues X-ray (s) Brems-strahung radiation.

3. Considering a projectile motion.Column – I Column – II

(A) Change in magnitude of momentum will bepresent

(p) At highest point parabolic path

(B) Maximum angular momentum about thepoint of throw

(q) 2mv sin between the point of throw andtarget.

(C) minimum velocity

(r) L =

3 22mv sin cos

g

(D) magnitude of change in momentum (s) along vertical direction.


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10

C C h h e e m m i i s s t t r r y y PART – II

SECTION – A



1. Which of the following is reactive intermediate for the following reaction?

O

2 4H SO

2 2HO CH CH OH

OO

(A)

OO+

OH

H

(B) OH

OO

(C)

OHO+

OH

H

(D)

OHO+

O

H

2. What is the expected order of reactivity of the following compounds in electrophilic nitration (morereactive, less reactive)?

Cl NHCOCH3 C2H5

(I) (II) (III) (IV)

3SO H

(A) I > II > III > IV (B) IV > I > II > III(C) III > IV > I > II (D) II > I > IV > III


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3. An electron is continuously accelerated in vacuum tube by applying potential difference. If its de-Broglie wavelength is decreased by 1%, the change in kinetic energy of the electron is nearly:(A) decreased by 1.0% (B) increased by 2.0%(C) increased by 1.0% (D) decreased by 2.0%

4. Quick lime; (CaO) is produced by heating limestone CaCO3 to drive off CO2 gas:

3 2CaCO CaO s CO g 1H 180 kJ mol

1S 150 JK

Assuming that variation of enthalpy change and entropy change with temperature to benegligible, which of the following is correct?(A) Decomposition of CaCO3(s) is always non-spontaneous at room temperature.(B) Decomposition of CaCO3(s) becomes spontaneous when temperature is less than 927

oC.(C) Decomposition of CaCO3(s) becomes non-spontaneous when temperature is greater than

1200oC.

(D) All of the above.

5. A doctor by mistake administers a dilute Ba(NO3)2 solution to a patient for radiographic

investigations. Which of the following should be the best to prevent the absorption of solublebarium and subsequent barium poisoning?(A) NaCl (B) Na2SO4 (C) Na2CO3 (D) NH4Cl

6. Match the products in the following reactions:List – I List – II

(1) 1:15 2PCl H O (a) N3P3Cl6 + 12 HCl

(2) 5 2PCl H O excess (b) [PCl4]+ [AlCl4]

(3) 5 3PCl AlCl (c) H3PO4 + HCl

(4) 5 4PCl NH Cl (d) POCl3 + HCl

(A) 1-d, 2-c, 3-b, 4-a (B) 1-b, 2-b, 3-d, 4-a(C) 1-d, 2-a, 3-b, 4-c (D) 1-c, 2-b, 3-d, 4-a

7. The magnetic momentum of K[Fe(CN)5(NO)] is:(A) 1.73 BM (B) 2.84 BM(C) 6.9 BM (D) Zero


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8. 6 5 2

Phenylhydrazine

C H NHNHGlucose X

PhenylhydrazineFructose Y

X and Y are:(A) Different osazones(B) Same osazones

(C) Each molecule of glucose reacts with 4 molecules of phenylhydrazine(D) Each molecule of fructose reacts with 2 molecules of phenylhydrazine

9. In which of the following -elimination occurs:(i)

3Me CO CHClBrI

H

Me H

Me

(ii)

Alc.KOH PhCl

O

(iii) Alc.KOH MeMe

Br

(iv)

2 2Ph CHCl NH

Me

H H

Me

(A) (i), (ii) (B) (i), (iv)(C) (ii), (iii) (D) (ii), (iv)


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Reasoning Type

This section contains 4 questions numbered 10 to 13. Each question contains STATEMENT-1(Assertion) and STATEMENT-2 (Reason). Each question has 4 choices (A), (B), (C) and (D) out of whichONLY ONE is correct.

10. STATEMENT-1: Bond energy of Cl – Cl bond is more than F – F bond.and

STATEMENT-2: Shorter the bond length more is the bond energy.(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for

Statement-1.(B) Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for

Statement-1.(C) Statement-1 is True, Statement -2 is False.(D) Statement-1 is False, Statement-2 is True.

11. STATEMENT-1: A gas can be easily liquefied at any temperature below its critical temperature.and

STATEMENT-2: Liquification of a gas takes place when the average kinetic energy of the

molecules is low.(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for




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12. STATEMENT-1: Para methoxy aniline undergoes faster diazotization than aniline.and

STATEMENT-2: Electron releasing group stabilizes diazonium salts.(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for



13. STATEMENT-1: The carboxylic and amino group in amino acid neutralize each other in aqueoussolution.and

STATEMENT-2: Amino acid forms Zwitterion by losing a proton from COOH group andaccepting a proton from H2O molecule.(A) Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for


Statement-1.

(C) Statement-1 is True, Statement -2 is False.(D) Statement-1 is False, Statement-2 is True.


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Comprehension Type



Consider the following mechanism of an aldol condensation reaction:

O

O

OH

O

O

H

H

OH

O

O

(I)(II)

O

O

OH

O

H2O

OO

H2O

(IV)(III)

O

OH

H2O

O

O

(X)

NaOH/CH3OH

Answer the following questions based on the above mechanism and your knowledge about aldolcondensation.

14. Which of the following statement regarding enolates I and II is true?(A) Enolate I is more stable than II, since it is formed by deprotonation of more acidic hydrogen.(B) Enolate I is more stable than II, since it is less substituted.(C) Enolate II is more stable than I, since it is formed by deprotonation of more stable than acidic

hydrogen.(D) Enolate II is more stable than I, since it is more substituted.

15. If all the alpha hydrogen in X is replaced by deuterium “D” atom. Which of the following would beobserved? (Assuming high concentration of base)(A) Rate of reaction would decrease since C – D bond is stronger than C – H bond.(B) Rate of reaction would increase since D is more acidic than H.(C) Rate of reaction would remains same since C – D bond is not broken in the rate determining

step.

(D) III would be formed more easily than IV.

16. How many different aldol products (excluding stereoisomers) are expected from intermolecularaldol condensation of X?(A) 2 (B) 4(C) 6 (D) 8


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16


The cell is 2Mg |Mg || Ag | Ag o

Ag |AgE 0.80V

2

o

Mg|MgE 2.37V

17. The value of log Kc is:(A) 107.45 (B) 80.5(C) 67.15 (D) 53.725

18. The maximum work obtained by the cell is:(A) 2 × 10

2 kJ (B) 3 × 10

2 kJ

(C) 5 × 102 kJ (D) 6 × 102 kJ

19. Calculate the Eo of cell.(A) –3.17 V (B) 3.17 V(C) 1.57 V (D) –1.57 V


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SECTION – B



1. Match the Column – I with Column – II:

Column – I(Reaction ) Column – II(Products)

(A)

Me

Me

Me CNa Br Me

(p) Me

Me

CH

Me

(B)Me

Me

Me

Br CNaMe

(q) No reaction

(C)Me CNa Br

(r)

Me

Me

Me

Me

(D)

Me CNa Br (s)

Me


Column – I(Orbitals) Column – II(Quantum No.)

(A) 2s (p) n 2, 0, m 0

(B) 2pz (q) n 2, 1, m 0

(C) 2 2x y4d (r) n 4, 1, m 2

(D) 2z4d (s) n 4, 2, m 0


Column – I Column – II

(A) NO2 (p) Paramagnetic

(B) NO (q) Dimerises on cooling

(C) Cl2O (r) Disproportionate either in cold or hot

water

(D) ClO2 (s) Act both oxidizing and reducing agent


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18

M M a a t t h h e e m m a a t t i i c c s s PART – III

SECTION – A



1. Consider a set {1, 2, 3, . . . ., 100}. The number of ways in which a number can be selected fromthe set so that it is of the form x

y, (where x, y, N and 2), is

(A) 12 (B) 16(C) 5 (D) 11

2. Solution set of [sin –1

x] > [ cos –1

x], where [.] denotes greatest integer function

(A) [sin 1, 1] (B)

1,

2

1

(C) (cos 1, sin 1) (D) none of these

3. The equation (1 + a2)x

2 + 2a

2x + a

2 + b

2 – 1 = 0 has roots of opposite sign if a + ib lies

(A) on a straight line x + y = 1(B) inside a circle of centre (0, 0) and radius 1(C) on a parabola of vertex (0, 0) and focal length 1(D) none of these

4. The complex number z satisfying |(z –2 + 3i)| = 6 and |z –4 –i| = |z –12 –i| are(A) one (B) two(C) three (D) none of these

5. f(x) = 20

2 2x 1 x x 1 , then(A) x = 1 is the point of local minima (B) x = –1/2 is the point of local minima(C) x = 1 is the point of local maxima (D) x = –1 is the point of local maxima


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6. If the tangent at the point (a sec , b tan ) to the hyperbola2 2

2 2

x y

a b = 1 meets the transverse

axis at T, then the distance of T from a focus of hyperbola is(A) a(e cos ) (B) ae

(C) b(e + cos ) (D) 2 2 2 2a e b cot

7. A bag contains 17 markers with numbers 1 to 17. A marker is drawn at random and thenreplaced; a second marker is drawn then the probability that first number is even and second isodd, is

(A)72

712 (B)

72

289

(C)9

34 (D) none of these

8. If in a triangle ABC, A 6

sin2 5

and 1I I = 9 (where I1, I2, I3 are ex–centres and I is

incentre), then circumradius R is equal to(A)

15

8 (B)

15

4

(C)15

2 (D)

4

15

9. If yr =

n r 1r 1

n

n ! C

r

, where n = kr (k is constant), then

nlim y

is equal to

(A) (k + 1) log(1 + k) – k (B) (k + 1) log(k – 1) + k(C) (k + 1) log(k – 1) – k (D) (k – 1) log(k – 1) + k

Reasoning Type

This section contains 4 questions numbered 10 to 13. Each question contains STATEMENT-1(Assertion) and STATEMENT-2 (Reason). Each question has 4 choices (A), (B), (C) and (D) out of whichONLY ONE is correct.

10. STATEMENT 1: Locus of P(z) is a straight line in the equation z – tz1 = (1 – t)z2, where z1, z2 arethe points A and B respectively in an argand planeSTATEMENT 2: A point dividing the two fixed point in the ratio m : n is collinear with the linethrough the given points(A) Both the statements are true and Statement 2 is correct explanation of Statement 1.(B) Both the Statements are true and Statement 2 is not the correct explanation of Statement 1.(C) Statement 1 is true and Statement 2 is false.(D) Statement 1 is false and Statement 2 is true.


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11. STATEMENT 1: If p < q and px2 + 4xy + qy2 + 4a(x + y + 1) = 0 represents pair of straight linesfor some R and a 0, then a p or a qSTATEMENT 2: The given equation has non-zero linear terms(A) Both the statements are true and Statement 2 is correct explanation of Statement 1.(B) Both the Statements are true and Statement 2 is not the correct explanation of Statement 1.(C) Statement 1 is true and Statement 2 is false.

(D) Statement 1 is false and Statement 2 is true.

12. STATEMENT 1: If f(x) = ax2 – bx + 2; a + b + 4 < 0 then exactly one root lies between – 1 and 0

STATEMENT 2: ab < 0(A) Both the statements are true and Statement 2 is correct explanation of Statement 1.(B) Both the Statements are true and Statement 2 is not the correct explanation of Statement 1.(C) Statement 1 is true and Statement 2 is false.(D) Statement 1 is false and Statement 2 is true.

13. STATEMENT 1: The order of the differential equation of family of circles touching a fixed straightline, which passes through origin is twoSTATEMENT 2: General equation of circle has three parameters so if conditions are given thenorder is two always

(A) Both the statements are true and Statement 2 is correct explanation of Statement 1.(B) Both the Statements are true and Statement 2 is not the correct explanation of Statement 1.(C) Statement 1 is true and Statement 2 is false.(D) Statement 1 is false and Statement 2 is true.

Comprehension Type



Read the following write up carefully and answer the following questions:If (x1, y1) is the image (reflection) of the point (x, y) in the line y = mx, then

2

1 2 2

1 m 2mx x y

1 m 1 m

and

2

1 2 2

2m m 1y x y

1 m 1 m

2

2 21

21

2 2

1 m 2m

x x1 m 1 m

y y2m m 1

1 m 1 m

X1 = AX X = A1X1

2

2 21

21

2 2

1 m 2m

xx 1 m 1 m

yy 2m m 1

1 m 1 m

, (since A2 = I).

14. The image of the parabola y2 = x in the line x + y + 4 = 0 is

(A) x

2

= (y + 4) (B) (x + 4)2

= (y + 4)(C) (x + 4)2 = y (D) none of these


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21

15. A ray moving along the line px + qy = 1, after striking a mirror placed along the line y = 3, isreflected along the line(A) px qy = 1 (B) px qy = 1 q(C) px qy = 1 6q (D) px qy = 1 4q

16. A tangent is drawn to the circle x2 + y

2 + 4x + 6y 7 = 0 at the point (2, – 1). The image of the

tangent in the line y = x + 2 touches the parabola(A) y

2 = 5x (B) 5y

2 = x

(C) y2 = –5x (D) 5y

2 = –x


Read the following write up carefully and answer the following questions:

Consider a three dimensional Cartesian system with origin at O and three rectangular coordinate axes x,y and z-axis. Suppose that the distance between two points P and Q in the space having theircoordinates (x1, y1, z1) and (x2, y2, z2) respectively be defined by the following formulad(P, Q) = |x2 x1| + |y2 y1| + |z2 z1|

Although the formula of distance between two points has been defined in a new way, yet the other

definitions remain same (like section formula, direction cosines etc.). So, in general equations of straightline in space, plane in space remain unchanged. Now answer the following questions.

17. If l, m, n represent direction cosines (if we can call it) of a vector OP

, then which of the followingrelations holds?(A) l

2 + m

2 + n

2 = 1 (B) l + m + n = 1

(C) |l + m + n| = 1 (D) |l| + |m| + |n| = 1

18. Locus of point P if d(O, P) = k, where k is a positive constant number, represents(A) a sphere of radius k(B) a set of eight planes forming an octahedron(C) a set of eight planes forming hexagonal prism

(D) an infinite cylinder of radius k

19. Let OABC represents a regular tetrahedron with edge length 2a and vertices A, B, C lying on x, yand z-axis respectively. Let P be a point inside the region of the tetrahedron satisfyingd(O, P) min{d(P, A), d(P, B), d(P, C)}. The maximum value of d(O, P) is(A) a (B) 2 a

(C)2a

3 (D)

4a

3


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SECTION – B



1. Match the following Column–I with Column–II


(A)

2 2 2 22 2

dx 1 dx

2a a xa x

is equal to (p) 2 2 2

xc

2a a x

(B)2 2 2

dx

x x a (q)

2 2

2

x a

a x

+ c

(C)2 2

2

a xdx

x

(r)

2 21a x xcos c

x a

(D)

2 2x adxx

(s)2 2 1 x

x a asec ca


Column – I Column – II (A) Area bounded by the parabola y

2 = 4x and the line y = x is

(p)1

2

(B) / 2

5 5

0

sin x cos x dx

is equal to(q) –22

(C) If S = 0 be the equation of the hyperbolax

2 + 4xy + 3y

2 – 4x + 2y + 1 = 0, then the value of k for

which S + k = 0 represents its asymptotes is

(r)8

3

(D) The value of for which ˆ ˆ ˆi 2 j k , lies in the plane

containing three points ˆ ˆ ˆi j k , ˆ ˆ ˆ2i 2j k and ˆ ˆ3i k is(s)

16

15



(A) 3x2 + 2 (b

2 + 1)x + b

2 3b + 2 = 0 will have roots of

opposite sign if b (p)2

, 13

(B) The probability of a problem being solved by 3 students are

1 1,

2 3

and (0, 1). Then probability that problem will be

solved

(q) [2 2 , )

(C) If 3 real numbers satisfy the equation x + y + z = 5 andxy + yz + zx = 8, then z (r)

71,

3

(D) The range of |sec x| + |cosec x| is (s) (1, 2)


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